College choices

Im a junior in high school and we just had our first college fair. I know that I would like to be a physicians assistant, and there are universities that have bachelor programs with a tie in pa program. The problem is I would like to stay in NY for school, and many schools that Im strongly considering(Binghamton, UBuffalo,) have great premed programs, but no pa programs and many schools with pa programs don’t accept transfers. So to conclude my question, is it required to do undergrad at the same place I plan on finishing a pa certification? I guess I’m just generally asking for other students pursuing a similar career or anyone with any thoughts.